{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T12:50:50Z","timestamp":1776689450914,"version":"3.51.2"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T00:00:00Z","timestamp":1776643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yunnan Fundamental Research Projects","award":["202401AT070359"],"award-info":[{"award-number":["202401AT070359"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Based on observations of real-world transport systems such as bus-subway systems, street-motorway networks, and rail-air transport frameworks, in which high-speed layers are typically constructed above pre-existing low-speed networks to alleviate congestion and improve efficiency, this study proposes a method for constructing multilayer transport networks by strategically deploying the high-speed layer according to node betweenness centrality in the underlying low-speed network. The concept of speed ratio is introduced to quantify the speed difference within the multilayer network. The multilayer network is integrated into the following model: the user equilibrium flow assignment strategy model based on the Bureau of Public Roads function. Utilizing network efficiency, high-speed layer utilization ratio, and proportion of congested edges as metrics, we analyze the impact of: (1) inter-tier speed ratio, (2) low-speed layer topology, and (3) interlayer transfer costs on system performance. Key findings indicate: Under a given traffic demand, increasing the inter-layer speed ratio elevates network efficiency while shifting congestion from lower to upper layers; incorporation of long-range connections improves efficiency, alleviating traffic congestion; introducing interlayer travel speed may enhance efficiency in specific parameter regimes.<\/jats:p>","DOI":"10.3390\/e28040469","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T12:01:22Z","timestamp":1776686482000},"page":"469","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Speed Ratio in a Novel Multilayer Traffic Network for Urban Congestion Relief and Efficiency Gain"],"prefix":"10.3390","volume":"28","author":[{"given":"Wenna","family":"Liu","sequence":"first","affiliation":[{"name":"Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China"},{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"},{"name":"Yunnan Key Laboratory of Complex Systems and Brain-Inspired Intelligence, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2946-9200","authenticated-orcid":false,"given":"Bo","family":"Yang","sequence":"additional","affiliation":[{"name":"Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China"},{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"},{"name":"Yunnan Key Laboratory of Complex Systems and Brain-Inspired Intelligence, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"046127","DOI":"10.1103\/PhysRevE.72.046127","article-title":"Statistical analysis of 22 public transport networks in Poland","volume":"72","author":"Sienkiewicz","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref_2","first-page":"630","article-title":"Study on the robustness of urban bus network based on the number of lines at a station","volume":"51","author":"Xie","year":"2022","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3678","DOI":"10.1016\/j.physa.2010.04.008","article-title":"The complexity and robustness of metro networks","volume":"389","author":"Derrible","year":"2010","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"046106","DOI":"10.1103\/PhysRevE.69.046106","article-title":"Statistical analysis of airport network of China","volume":"69","author":"Li","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"036106","DOI":"10.1103\/PhysRevE.67.036106","article-title":"Small-world properties of the Indian railway network","volume":"67","author":"Sen","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2150151","DOI":"10.1142\/S0217979221501514","article-title":"Topologic characteristics and sustainable growth of worldwide urban rail networks","volume":"35","author":"Ding","year":"2021","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/j.proeng.2016.01.290","article-title":"Analysis of urban road traffic network based on complex network","volume":"137","author":"Tian","year":"2016","journal-title":"Procedia Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, Y., Wang, T., Zhao, Y., and Yang, B. (2025). Identifying polycentric urban structure using the minimum cycle basis of road network as building blocks. Entropy, 27.","DOI":"10.3390\/e27060618"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44359","DOI":"10.1038\/srep44359","article-title":"A multilayer perspective for the analysis of urban transportation systems","volume":"7","author":"Aleta","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.dcan.2018.10.011","article-title":"Traffic dynamics on multilayer networks","volume":"6","author":"Wu","year":"2020","journal-title":"Digit. Commun. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2450041","DOI":"10.1142\/S0129183124500414","article-title":"Construction and traffic dynamics analysis of multi-layer network model with different speed physical layers","volume":"35","author":"Ma","year":"2024","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"046108","DOI":"10.1103\/PhysRevE.73.046108","article-title":"Efficient routing on complex networks","volume":"73","author":"Yan","year":"2006","journal-title":"Phys. Rev. E"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevE.100.012310","article-title":"Effective traffic-flow assignment strategy on multilayer networks","volume":"100","author":"Gao","year":"2019","journal-title":"Phys. Rev. E"},{"key":"ref_14","first-page":"1697","article-title":"Traffic dynamics on multilayer networks with different speeds","volume":"69","author":"Ma","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_15","first-page":"3149","article-title":"An effective resource allocation strategy for three-layer networks","volume":"70","author":"Ma","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"113110","DOI":"10.1016\/j.chaos.2023.113110","article-title":"The influence of edge-adding strategy on traffic capacity of multilayer network","volume":"168","author":"Ma","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1209\/epl\/i2005-10551-x","article-title":"Congestion in different topologies of traffic networks","volume":"74","author":"Wu","year":"2006","journal-title":"Europhys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.physa.2007.10.014","article-title":"Optimal traffic networks topology: A complex networks perspective","volume":"387","author":"Wu","year":"2008","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1007\/s11071-012-0411-5","article-title":"Correlated scale-free network with community: Modeling and transportation dynamics","volume":"69","author":"Sun","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s11071-012-0729-z","article-title":"Traffic dynamics in the correlated networks with user equilibrium","volume":"72","author":"Sun","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"178902","DOI":"10.7498\/aps.62.178902","article-title":"Congestion and efficiency in complex traffic and transportation networks","volume":"62","author":"Xiao","year":"2013","journal-title":"Acta Phys. Sin."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.physa.2014.03.023","article-title":"Network congestion analysis of gravity generated models","volume":"405","author":"Maniadakis","year":"2014","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1109\/TITS.2015.2498186","article-title":"Congestion avoidance routing based on large-scale social signals","volume":"17","author":"He","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7506","DOI":"10.1109\/ACCESS.2019.2959654","article-title":"Research on a model of node and path selection for traffic network congestion evacuation based on complex network theory","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"102719","DOI":"10.1016\/j.tre.2022.102719","article-title":"A new network equilibrium flow model: User-equilibrium with quantity adjustment","volume":"163","author":"Huang","year":"2022","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2014.07.001","article-title":"The structure and dynamics of multilayer networks","volume":"544","author":"Boccaletti","year":"2014","journal-title":"Phys. Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1093\/comnet\/cnu016","article-title":"Multilayer networks","volume":"2","author":"Kivela","year":"2014","journal-title":"J. Complex Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"128703","DOI":"10.1103\/PhysRevLett.109.128703","article-title":"Transport on coupled spatial networks","volume":"109","author":"Morris","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"127025","DOI":"10.1016\/j.physa.2022.127025","article-title":"The influence of average speed ratio on multilayer traffic network","volume":"594","author":"Ding","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"062813","DOI":"10.1103\/PhysRevE.89.062813","article-title":"Traffic congestion in interconnected complex networks","volume":"89","author":"Tan","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"39175","DOI":"10.1038\/srep39175","article-title":"Transportation dynamics on coupled networks with limited bandwidth","volume":"6","author":"Li","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"108701","DOI":"10.1103\/PhysRevLett.116.108701","article-title":"Congestion induced by the structure of multiplex networks","volume":"116","author":"Gomez","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"L012201","DOI":"10.1103\/PhysRevE.111.L012201","article-title":"Strategic variability in routing: Enhancing network performance in two-layer traffic systems","volume":"111","author":"Cheong","year":"2025","journal-title":"Phys. Rev. E"},{"key":"ref_34","first-page":"223","article-title":"Exploring the multi-Layer structural properties of the bus-subway transportation network of Shanghai","volume":"15","author":"Tang","year":"2023","journal-title":"J. Geogr. Inf. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"026101","DOI":"10.1103\/PhysRevE.84.026101","article-title":"Onset of cooperation between layered networks","volume":"84","author":"Gu","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.tre.2016.03.009","article-title":"Analysis of the Chinese airline network as multi-layer networks","volume":"89","author":"Du","year":"2016","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"105758","DOI":"10.1016\/j.cnsns.2021.105758","article-title":"Efficient traffic-aware routing strategy on multilayer networks","volume":"98","author":"Hu","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2150584","DOI":"10.1142\/S0217984921505849","article-title":"An efficient routing strategy for coupled spatial networks","volume":"36","author":"Jing","year":"2022","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.trb.2006.02.008","article-title":"A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration","volume":"40","author":"Dial","year":"2006","journal-title":"Transp. Res. 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